Global and Local Nonlinear System Responses under Narrowband Random Excitations. I: Semianalytical Method
Publication: Journal of Engineering Mechanics
Volume 133, Issue 1
Abstract
A single-degree-of-freedom nonlinear structural system under narrowband random excitation can exhibit very complex global and local response behaviors. In order to develop a stochastic method to analyze the nonlinear responses, the system under deterministic excitation is first modeled and examined in the primary and subharmonic resonance regions. Typical response behaviors including coexistence of attractors and (global) jump phenomena are observed. Governing equations of the probability for the response–amplitude perturbations (a local transition) within an attraction domain and a jump between different attraction domains (a global transition) are derived under the assumption of a stationary Markov condition. The overall response–amplitude probability distribution is obtained by applying the Bayes formula to the two types of response transition probability distributions. In this study, we focus on understanding the physics of the transitions using the proposed probability method.
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Acknowledgments
Financial support from the United States Office of Naval Research (Grant Nos. ONRN00014-92-J-1221 and ONRN00014-04-10008) is gratefully acknowledged.
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Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 133 • Issue 1 • January 2007
Pages: 22 - 29
Copyright
© 2007 ASCE.
History
Received: Dec 19, 2005
Accepted: Apr 19, 2006
Published online: Jan 1, 2007
Published in print: Jan 2007
Notes
Note. Associate Editor: Ross Barry Corotis
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